Problem: Solve for $x$ and $y$ using elimination. ${5x+5y = 60}$ ${-2x+4y = -6}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $-4$ and the bottom equation by $5$ ${-20x-20y = -240}$ $-10x+20y = -30$ Add the top and bottom equations together. $-30x = -270$ $\dfrac{-30x}{{-30}} = \dfrac{-270}{{-30}}$ ${x = 9}$ Now that you know ${x = 9}$ , plug it back into $\thinspace {5x+5y = 60}\thinspace$ to find $y$ ${5}{(9)}{ + 5y = 60}$ $45+5y = 60$ $45{-45} + 5y = 60{-45}$ $5y = 15$ $\dfrac{5y}{{5}} = \dfrac{15}{{5}}$ ${y = 3}$ You can also plug ${x = 9}$ into $\thinspace {-2x+4y = -6}\thinspace$ and get the same answer for $y$ : ${-2}{(9)}{ + 4y = -6}$ ${y = 3}$